a Decision-Tree based Moment-of-Fluid (DTMOF) Method in 3D rectangular hexahedrons

The moment-of-fluid (MOF) method is an extension of the volume-of-fluid method with piecewise linear interface construction (VOF-PLIC). By minimizing the least square error of the centroid of the cutting polyhedron, the MOF method reconstructs the linear interface without using any neighboring information. Traditional MOF involves iteration while finding the optimized linear reconstruction. Here, we propose an alternative approach based on a machine learning algorithm: Decision Tree algorithm. A training data set is generated from a list of random cuts of a unit cube by plane. The Decision Tree algorithm extracts the input-output relationship from the training data, so that the resulting function determines the normal vector of the reconstruction plane directly, without any iteration. The present method is tested on a range of popular interface advection test problems. Numerical results show that our approach is much faster than the iteration-based MOF method while provides compatible accuracy with the conventional MOF method.